[FOM] Weaker foundations for FLT

[praatika@mappi.helsinki.fi]

Solovay wrote:
 
> As the cited book shows the Wiles-Taylor proof is a truly
> enormous beast. The work naturally seems to be carried out in third 
> order number theory, and to compress it into PA seems a heroic if not 
> impossible task.

Not that I know much about FLT and related issues, but nevertheless... 
this is not necessarily a problem: Feferman has formulated certain theories 
of finite types, suitable for a direct formalization of ordinary 
mathematics, which are conservative over PA. If the third order stuff can 
be carried out in such a system, it follows that FLT is after all provable 
in PA.  
Right?

Best, Panu


Panu Raatikainen
Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy
Department of Philosophy, 
University of Helsinki
Finland

Visiting Fellow, 
Institute of Philosophy,
School of Advanced Studies, 
University of London

E-mail: panu.raatikainen at helsinki.fi
 
http://www.helsinki.fi/collegium/eng/Raatikainen/raatikainen.htm